Weight combinatorics. In this section we start with an irregular weight of the form (k, 0) and associate several regular weights to it. In the next section we then prove the main theorem,
Weight combinatorics Sample Clauses
Related to Weight combinatorics
Stock Splits and Combinations If the Company shall at any time subdivide or combine its outstanding shares of Common Stock, this Warrant shall, after that subdivision or combination, evidence the right to purchase the number of shares of Common Stock that would have been issuable as a result of that change with respect to the shares of Common Stock which were purchasable under this Warrant immediately before that subdivision or combination. If the Company shall at any time subdivide the outstanding shares of Common Stock, the Warrant Exercise Price then in effect immediately before that subdivision shall be proportionately decreased, and, if the Company shall at any time combine the outstanding shares of Common Stock, the Warrant Exercise Price then in effect immediately before that combination shall be proportionately increased. Any adjustment under this section shall become effective at the close of business on the date the subdivision or combination becomes effective.
Splits and Combinations (a) Subject to Section 5.9(d), Section 6.6 and Section 6.9 (dealing with adjustments of distribution levels), the Partnership may make a Pro Rata distribution of Partnership Securities to all Record Holders or may effect a subdivision or combination of Partnership Securities so long as, after any such event, each Partner shall have the same Percentage Interest in the Partnership as before such event, and any amounts calculated on a per Unit basis (including any Common Unit Arrearage or Cumulative Common Unit Arrearage) or stated as a number of Units (including the number of Subordinated Units that may convert prior to the end of the Subordination Period) are proportionately adjusted. (b) Whenever such a distribution, subdivision or combination of Partnership Securities is declared, the General Partner shall select a Record Date as of which the distribution, subdivision or combination shall be effective and shall send notice thereof at least 20 days prior to such Record Date to each Record Holder as of a date not less than 10 days prior to the date of such notice. The General Partner also may cause a firm of independent public accountants selected by it to calculate the number of Partnership Securities to be held by each Record Holder after giving effect to such distribution, subdivision or combination. The General Partner shall be entitled to rely on any certificate provided by such firm as conclusive evidence of the accuracy of such calculation. (c) Promptly following any such distribution, subdivision or combination, the Partnership may issue Certificates to the Record Holders of Partnership Securities as of the applicable Record Date representing the new number of Partnership Securities held by such Record Holders, or the General Partner may adopt such other procedures that it determines to be necessary or appropriate to reflect such changes. If any such combination results in a smaller total number of Partnership Securities Outstanding, the Partnership shall require, as a condition to the delivery to a Record Holder of such new Certificate, the surrender of any Certificate held by such Record Holder immediately prior to such Record Date. (d) The Partnership shall not issue fractional Units upon any distribution, subdivision or combination of Units. If a distribution, subdivision or combination of Units would result in the issuance of fractional Units but for the provisions of this Section 5.9(d), each fractional Unit shall be rounded to the nearest whole Unit (and a 0.5 Unit shall be rounded to the next higher Unit).
Stock Dividends, Splits and Combinations If the Company issues solely shares of Common Stock as a dividend or distribution on all or substantially all shares of the Common Stock, or if the Company effects a stock split or a stock combination of the Common Stock (in each case excluding an issuance solely pursuant to a Common Stock Change Event, as to which Section 5.09 will apply), then the Conversion Rate will be adjusted based on the following formula: where: CR0 = the Conversion Rate in effect immediately before the Open of Business on the Ex-Dividend Date for such dividend or distribution, or immediately before the Open of Business on the effective date of such stock split or stock combination, as applicable; CR1 = the Conversion Rate in effect immediately after the Open of Business on such Ex-Dividend Date or effective date, as applicable; OS0 = the number of shares of Common Stock outstanding immediately before the Open of Business on such Ex-Dividend Date or effective date, as applicable, without giving effect to such dividend, distribution, stock split or stock combination; and OS1 = the number of shares of Common Stock outstanding immediately after giving effect to such dividend, distribution, stock split or stock combination. If any dividend, distribution, stock split or stock combination of the type described in this Section 5.05(A)(i) is declared or announced, but not so paid or made, then the Conversion Rate will be readjusted, effective as of the date the Board of Directors determines not to pay such dividend or distribution or to effect such stock split or stock combination, to the Conversion Rate that would then be in effect had such dividend, distribution, stock split or stock combination not been declared or announced.
Adjustment for Stock Splits and Combinations If the Company shall at any time or from time to time after the date on which this Warrant was first issued (the "Original Issue Date") effect a subdivision of the outstanding Common Stock, the Purchase Price then in effect immediately before that subdivision shall be proportionately decreased. If the Company shall at any time or from time to time after the Original Issue Date combine the outstanding shares of Common Stock, the Purchase Price then in effect immediately before the combination shall be proportionately increased. Any adjustment under this paragraph shall become effective at the close of business on the date the subdivision or combination becomes effective.
Combinations and Split-ups of Receipts Upon surrender of a Receipt or Receipts at the Depositary Office or such other office as the Depositary may designate for the purpose of effecting a split-up or combination of Receipts, subject to the terms and conditions of this Deposit Agreement, the Depositary shall execute and deliver a new Receipt or Receipts in the authorized denominations requested evidencing the same aggregate number of Depositary Shares evidenced by the Receipt or Receipts surrendered.
Stock Splits, Dividends and Combinations In the event that the Company shall at any time subdivide the outstanding shares of Common Stock, or shall issue a stock dividend on its outstanding shares of Common Stock, the number of Warrant Shares issuable upon exercise of this Warrant immediately prior to such subdivision or to the issuance of such stock dividend shall be proportionately increased, and the Exercise Price shall be proportionately decreased, and in the event that the Company shall at any time combine the outstanding shares of Common Stock, the number of Warrant Shares issuable upon exercise of this Warrant immediately prior to such combination shall be proportionately decreased, and the Exercise Price shall be proportionately increased, effective at the close of business on the date of such subdivision, stock dividend or combination, as the case may be.
Adjustments for Stock Splits and Combinations If the Maker shall at any time or from time to time after the Closing Date (but whether before or after the Issuance Date) effect a split of the outstanding Common Stock, the applicable Conversion Price in effect immediately prior to the stock split shall be proportionately decreased. If the Maker shall at any time or from time to time after the Closing Date (but whether before or after the Issuance Date), combine the outstanding shares of Common Stock, the applicable Conversion Price in effect immediately prior to the combination shall be proportionately increased. Any adjustments under this Section 3.4(a)(i) shall be effective at the close of business on the date the stock split or combination occurs.
Initial Business Combination/Distribution Procedure The Company may consummate the Initial Business Combination and conduct redemptions of Common Stock for cash upon consummation of such Initial Business Combination without a stockholder vote pursuant to Rule 13e-4 and Regulation 14E of the Exchange Act, including the filing of tender offer documents with the Commission. Such tender offer documents will contain substantially the same financial and other information about the Initial Business Combination and the redemption rights as is required under the Commission’s proxy rules and will provide each stockholder of the Company with the opportunity prior to the consummation of the Initial Business Combination to redeem the Common Stock held by such stockholder for an amount of cash equal to (A) the aggregate amount then on deposit in the Trust Account as of two Business Days prior to the consummation of the Initial Business Combination representing (x) the proceeds held in the Trust Account from the Offering and the sale of the Private Placement Warrants and (y) any interest, divided by (B) the total number of Public Shares then outstanding. In the event the Company conducts redemptions pursuant to the tender offer rules, the Company’s offer to redeem will remain open for at least 20 Business Days, in accordance with Rule 14e-1(a) under the Exchange Act, and the Company will not be permitted to complete the Initial Business Combination until the expiration of the tender offer period. If, however, the Company elects not to file such tender offer documents, a stockholder vote is required by law or stock exchange listing requirement in connection with the Initial Business Combination, or the Company decides to hold a stockholder vote for business or other legal reasons, the Company will submit such Initial Business Combination to the Company’s stockholders for their approval (“Business Combination Vote”). The company will give not less than 10 days nor more than 60 days prior written notice of any such meeting, if required, at which a Business Combination Vote shall be taken. With respect to the Business Combination Vote, the Sponsor and the Company’s initial stockholders, executive officers and directors have agreed to vote all of their Founder Shares and Public Shares in favor of the Company’s initial Business Combination. If the Company seeks stockholder approval of the Initial Business Combination, the Company will offer to each Public Stockholder holding shares of Common Stock the right to have its shares redeemed in conjunction with a proxy solicitation pursuant to the proxy rules of the Commission at a per share redemption price (the “Redemption Price”) equal to (I) the aggregate amount then on deposit in the Trust Account as of two Business Days prior to the consummation of the Initial Business Combination representing (1) the proceeds held in the Trust Account from the Offering and the sale of the Private Placement Warrants and (2) any interest, divided by (II) the total number of Public Shares then outstanding. The Company may proceed with such Initial Business Combination only if a majority of the shares voted are voted to approve such Initial Business Combination. If, after seeking and receiving such stockholder approval, the Company elects to so proceed, it will redeem shares, at the Redemption Price, from those Public Stockholders who affirmatively requested such redemption. Only Public Stockholders holding Common Stock who properly exercise their redemption rights, in accordance with the applicable tender offer or proxy materials related to such Initial Business Combination, shall be entitled to receive distributions from the Trust Account in connection with an Initial Business Combination, and the Company shall pay no distributions with respect to any other holders or shares of capital stock of the Company in connection therewith. In the event that the Company does not effect an Initial Business Combination within the time period set forth in the Amended and Restated Certificate of Incorporation, the Company will (i) cease all operations except for the purpose of winding up, (ii) as promptly as reasonably possible but not more than ten (10) Business Days thereafter, redeem 100% of the Public Shares, at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including any interest (which shall be net of amounts withdrawn to pay taxes and up to $100,000 of interest to pay dissolution expenses), divided by the number of then outstanding Public Shares, which redemption will completely extinguish Public Stockholders’ rights as stockholders (including the right to receive further liquidation distributions, if any), subject to applicable law, and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining stockholders and the Company’s board of directors, dissolve and liquidate, subject in each case to the Company’s obligations under Delaware law to provide for claims of creditors and the requirements of other applicable law. Only Public Stockholders holding Common Stock included in the Securities shall be entitled to receive such redemption amounts and the Company shall pay no such redemption amounts or any distributions in liquidation with respect to any other shares of capital stock of the Company. The Company will not propose any amendment to the Amended and Restated Certificate of Incorporation to modify the substance or timing of the Company’s obligation to provide for the redemption of the Public Shares in connection with an Initial Business Combination or to redeem 100% of its Public Shares if it does not complete its initial business combination within the time period set forth in the Amended and Restated Certificate of Incorporation, unless it provides its public stockholders with the opportunity to redeem their shares of Class A common stock upon approval of any such amendment, as described in the Statutory Prospectus and Prospectus.
Stock Dividends, Subdivisions and Combinations If at any time the Issuer shall: (i) make or issue or set a record date for the holders of the Common Stock for the purpose of entitling them to receive a dividend payable in, or other distribution of, shares of Common Stock, (ii) subdivide its outstanding shares of Common Stock into a larger number of shares of Common Stock, or (iii) combine its outstanding shares of Common Stock into a smaller number of shares of Common Stock, then (1) the number of shares of Common Stock for which this Warrant is exercisable immediately after the occurrence of any such event shall be adjusted to equal the number of shares of Common Stock which a record holder of the same number of shares of Common Stock for which this Warrant is exercisable immediately prior to the occurrence of such event would own or be entitled to receive after the happening of such event, and (2) the Warrant Price then in effect shall be adjusted to equal (A) the Warrant Price then in effect multiplied by the number of shares of Common Stock for which this Warrant is exercisable immediately prior to the adjustment divided by (B) the number of shares of Common Stock for which this Warrant is exercisable immediately after such adjustment.
Combination Products If a LICENSED PRODUCT is sold to any third party in combination with other products, devices, components or materials that are capable of being sold separately and are not subject to royalties hereunder (“OTHER PRODUCTS,” with the combination of products being referred to as “COMBINATION PRODUCTS” and the Other Product and Licensed Product in such Combination Product being referred to as the “COMPONENTS”), the NET SALES of such LICENSED PRODUCT included in such COMBINATION PRODUCT shall be calculated by multiplying the NET SALES of the COMBINATION PRODUCT by the fraction A/(A+B), where A is the average NET SALES price of such LICENSED PRODUCT in the relevant country, as sold separately, and B is the total average NET SALES price of all OTHER PRODUCTS in the COMBINATION PRODUCT in the relevant country, as sold separately. If, in any country, any COMPONENT is not sold separately, NET SALES for royalty determination shall be determined by the formula [C / (C+D)], where C is the aggregate average fully absorbed cost of the Licensed Product components during the prior Royalty Period and D is the aggregate average fully absorbed cost of the other essential functional components during the prior Royalty Period, with such costs being determined in accordance with generally accepted accounting principles. To the extent that any SUBLICENSE INCOME relates to a COMBINATION PRODUCT or is otherwise calculated based on the value of one or more licenses or intellectual property rights held by the COMPANY, an AFFILIATE or SUBLICENSEE, COMPANY shall determine in good faith and report to THE PARTIES the share of such payments reasonably attributable to COMPANY’s or such AFFILIATE’s sublicense of the rights granted hereunder, based upon their relative importance and proprietary protection, which portion shall be the SUBLICENSE INCOME. THE PARTIES shall have the right to dispute such sharing determination in accordance with the dispute provisions of the AGREEMENT.
