INVERSE-CONJUGATE COMPOSITIONS INTO PARTS OF SIZE AT MOST k
نویسندگان
چکیده
An inverse-conjugate composition of a positive integer m is an ordered partition of m whose conjugate coincides with its reversal. In this paper we consider inverseconjugate compositions in which the part sizes do not exceed a given integer k. It is proved that the number of such inverse-conjugate compositions of 2n − 1 is equal to 2F n , where F (k) n is a Fibonacci k-step number. We also give several connections with other types of compositions, and obtain some analogues of classical combinatorial identities.
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